Multi-layered shields covering stethoscopes (and other instruments), as described in U.S. Pat. No. 6,009,971, must be individually removable, from the outermost shield down to the innermost shield nearest to the diaphragm of the stethoscope. This may be difficult to achieve in that pulling on the outermost shield to remove it may inadvertently cause the removal simultaneously of one or more shields lying between the outermost shield and the diaphragm of the stethoscope. The method described herein shows how to construct and use multi-layered stethoscope shields to avoid this problem and to ensure that the shields can be individually removed (and discarded) in sequence from the outermost shield down to the last shield nearest to the stethoscope diaphragm. Also disclosed is a structure of a plurality of shields which is suitable for such individual removal.